+1222 A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, 4, 6, 6, 1, 5 is one possible sequence.)
+1897 First, we need to calculate the total possible number of rolls. Since the dice is rolled 7 times, we have \(7!\) total rolls.
However, since there are duplicates with two 6s being rolled, we must divide by 2! to avoid overcounting.
Thus, we just have
\(7! / 2! = 2520\)
So the answer is 2520.
Thanks! :)
